Converters are widely used in controlling electrical loads. Converters may be employed in feeding electrical power to and from an electrical machine, a load or an AC grid. Typically, the converter is referred to as an inverter when it is used to control a motor or a load, and a (grid-connected) converter when it is used for feeding power to and from an AC grid. An example of a two-level three-phase voltage source inverter with an output LC filter driving an induction motor is provided in FIG. 1.
Typical control problems of power electronic systems include the following. For example, for a converter driving an electrical machine, the stator currents need to be regulated along their reference trajectories. In case of a drive system with an intermediate LC filter (see FIG. 1), also the filter capacitor voltages and the converter currents should be regulated. Moreover, during steady-state operation, transients and faults, the total harmonic distortion (THD) of the load currents should be minimized. This is equivalent to minimizing the root mean squared (rms) current error. Furthermore, for grid-side converters, the harmonic spectra of the grid currents and voltages should meet the relevant grid code. This implies a harmonic spectrum with harmonics at odd non-triplen integer multiples of the fundamental frequency and operation at a constant switching frequency. Typically, amplitudes of higher-order harmonics should be small. Moreover, when an LC filter is employed, the ratio between the switching frequency and the frequency of the LC filter resonance is of prime importance. In order to minimize the size of this filter, the mentioned ratio should be as small as possible. Any ratio below three is considered to be small. Furthermore, in a converter, a fast closed-loop control is required to quickly compensate for changes in the load, such as torque and power steps, as well as for fast rejection of disturbances, such as dc-link voltage ripple.
Considering all the above, it is apparent that a suitable controller should successfully meet all the control objectives, which in many cases compete with each other. Control designers most commonly resort to simplifications of the control problem at hand as well as of the model of the power electronic system. Specifically, given that power electronic systems are nonlinear multiple-input, multiple output (MIMO) systems with constraints on input variables (such as integer constraints or duty cycle constraints), state variables (such as current constraints) and output variables, the MIMO control problem is typically decomposed into multiple single-input, single-output (SISO) loops, which are arranged in a cascaded manner according to the dominant time constant of each loop. Following, to conceal the switching nature of the system, the concept of averaging and pulse width modulation (PWM) is employed. This gives rise to indirect control, which is presented in FIG. 2. Cascaded SISO loops and a PWM stage enable the use of linear controllers, such as conventional proportional-integral-derivative (PID) controllers. Such controllers are typically augmented by additional anti-windup mechanisms and rate limiters. In case of LC filters, the inner (current) control loop is augmented with an active damping loop to dampen the system resonance introduced by the filter.
Although indirect control techniques work well at steady-state operation, during transients and faults, the different control loops are often poorly decoupled, interacting with each other adversely. This implies that the bandwidth of the controller should be reduced in order to avoid stability issues, which, in turn, limits the system performance. Moreover, since controllers of this type are usually tuned to achieve satisfactory performance only in a narrow operating range, when operating at a point outside this range the performance tends to deteriorate significantly. To avoid the latter, gain scheduling is adopted, which further complicates the tuning of the control loops and renders the whole design procedure cumbersome.
Moreover, when MIMO systems like a converter with an LC filter are to be controlled, the controller design should be relatively straightforward. The control of the output variables (such as load currents, capacitor voltages, converter currents, etc.) should be performed in one loop, while additional damping loops that further complicate the design are to be avoided.
As can be understood from the above, a new MIMO control approach is required that tackles all the control objectives in one computational stage.